Question 1188487
2012 is the base year.


when the year is:


2012, x = 2012 - 2012 = 0, and n(x) = 100 * (3 * 0 + 20) = 100 * 20 = 2000
2013, x = 2012 - 2012 = 1, and n(x) = 100 * (3 * 1 + 20) = 100 * 23 = 2300
2018, x = 2018 - 2012 = 6, and n(x) = 100 * (3 * 6 + 20) = 100 * 38 = 3800
2021, x = 2021 - 2012 = 9, and n(x) = 100 * (3 * 9 + 20) = 100 * 47 = 4700


the equation of n(x) = 100 * (3 * x + 20) can be graphed.


i replaced n(x) with y and graphed it, as shown below.


<img src = "http://theo.x10hosting.com/2021/120501.jpg" >


the graphing software i used can be found at <a href = "https://www.desmos.com/calculator" target = "_blank">https://www.desmos.com/calculator</a>


this is a linear equations.
it can be transformed into the slope intercept form of a linear equation as follows:


replace n(x) with y.
start with y = 100 * (3 * x + 20)
simplify to get:
y = 100 * 3 * x + 100 * 20
simplify further to get:
y = 300 * x + 2000
the equation is now in slope intercept form.
the slope is 300 and the y-intercept is 2000.
this means that y = 2000 when x = 0 (y-intercept) and, for every increase of 1 in the value of x, the corresponding value of y increased by 100.
x = 0, y = 2000
x = 1, y = 2300
x = 2, y = 2600
etc.


the annual rate of change is the slope which is equal to 300.